https://hal-hec.archives-ouvertes.fr/hal-01941517Mongin, PhilippePhilippeMonginHEC Paris - Recherche - Hors Laboratoire - HEC Paris - Ecole des Hautes Etudes CommercialesBayesian Decision Theory and Stochastic IndependenceHAL CCSD2017Stochastic IndependenceProbabilistic IndependenceBayesian Decision TheorySavage[SHS.GESTION] Humanities and Social Sciences/Business administrationHaldemann, Antoine2018-12-01 13:42:582022-06-25 10:56:192018-12-01 13:42:58enPreprints, Working Papers, ...1Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory.